A Hamiltonian Study Of The Stability and Bifurcations For The Satellite Problem

TL;DR

This paper analyzes the stability and bifurcations of satellite motion using Hamiltonian dynamics, introducing new methods for stability analysis and identifying novel equilibrium states for axisymmetric bodies.

Contribution

It applies the Reduced Energy Momentum method to satellite problems, explicitly finds new relative equilibria, and examines their stability and bifurcation behavior.

Findings

Existence of new relative equilibria

Stability analysis of these equilibria

Bifurcation patterns identified for axisymmetric bodies

Abstract

We study the dynamics of a rigid body in a central gravitational field modeled as a Hamiltonian system with continuous rotational symmetries following the geometrical framework of Wang et al. Novelties of our work are the use the Reduced Energy Momentum for the stability analysis and the treatment of axisymmetric bodies. We explicitly show the existence of new relative equilibria and study their stability and bifurcation patterns.